\section{Nonmenclature}

\begin{tabular}{ll}
    $[B]$      & Displacement-to-Strain Matrix        \\
    $[D]$      & Material Matrix                      \\
    $E$        & Young's Modulus ($F/L^2$)            \\
    $\{F\}$    & Applied force vector                 \\
    $\{F_g\}$  & Global  applied force vector         \\
    $\{F_a\}$  & Reduced applied force vector         \\
    $\{f\}$    & Generalized (Modal) force vector     \\
    $G$        & Shear Modulus ($F/L^2$)              \\
    $[J]$      & Jacobian Matrix                      \\
    $[K]$      & Stiffness matrix                     \\
    $[K_e]$    & Element stiffness matrix ( $ F/ L^2$ ) \\
    $[K_{gg}]$ & Global  Stiffness Matrix             \\
    $[K_{aa}]$ & Reduced Stiffness Matrix             \\
    $k$        & Spring stiffness ( $ F/L^2$ )        \\
    $L$        & Length (L)                           \\
    $L,M,N$    & X,Y,Z Moment (FL)                    \\
    $M_x$,$M_y$,$M_z$    & X,Y,Z Moment (FL)           \\
    $[M]$      & Mass Matrix                          \\
    $[M_L]$    & Lumped Mass Matrix                   \\
    $[N]$      & Shape Function Matrix                \\
    $m$        & mass (M)                             \\
    nsm        & non-structural mass (M)              \\
    $[T]$      & Transformation matrix                \\
    $t$        & thickness (L)                        \\
    $T$        & translation (L)                      \\
    $R$        & rotation (L/radians)                 \\
    $u$        & generalized load (translation, rotation) \\
    $X,Y,Z$    & X,Y,Z Force (F)                      \\
    $F_x$,$F_y$,$F_z$    & X,Y,Z Force (F)             \\
    $x,y,z$    & displacement (L)                     \\
    $\{x\}$    & generalized load (translation, rotation) \\
    $V$        & Volume  ( $L^3$ )                     \\
    $V_i$      & $i^{th}$ Volume  ( $L^3$ )            \\
    $\epsilon$ & strain, shear strain ($\Delta L/L$)   \\
    $\gamma$   & shear strain ($F/L^2$)                \\
    $\nu$      & Poisson's ratio                       \\
    ${\Omega}$ & Natural frequencies ($Hz$)            \\
    $\omega$   & natural frequency ($Hz$)              \\
    $\rho$     & density ($M/L^3$)                     \\
    $\sigma_{ij}$ & normal stress, shear stress ($F/L^2$) \\
    $\tau_{ij}$   & shear stress ($F/L^2$)                \\
    $\theta$   & rotation (radians)
\end {tabular}
